ThinkThankThunk

Dealing with the fear of being a boring teacher.

7

Inquiry Stylee: Gravity Smorgasbord

Teaching gravity is rough. By that I mean it’s quite difficult to have students really interact with it in a sandbox setting.  It’s ubiquitous; it’d be kind of like trying to teach fish about the properties of water: “Yeah, yeah, it’s wet, super important, makes ice, got it.”

Then there’s the banality that is gravity near the surface of a planet: The theory for this force is so simple, it’s often quite difficult for students to respect:

W=mg

The more mass you have, the more weight you have, surprise! At this point we’ve proven six ways that g is the acceleration from gravity on any object, so they’re even less impressed.

Invitation:

The invitation begins with the question: who has a bigger g: Earth or Saturn? Saturn. So, the force I feel from Saturn (mg) is bigger than the force I feel from the Earth? Err, yes? No? Yellow?? (thrown from bridge)

Such a stupid question leads to brilliant responses from the kids:

“Mr. C, I’m pretty sure how far away you are from Saturn matters.” One ingenious little cherub chirps.

“I’m not so sure… AHHHHHHOMGMYLEGS!” Cornally feigns being sucked out the window into space towards Saturn. “No, wait,” climbing down from the window, “you’re right.”

F_G = \frac{Gm_1m_2}{r^2}

There’s nothing like an inverse square law to get the blood pumping. They make me giddy. Indeed the distance matters, and the farther you are, the lower the force. This is nice, but if we’re going to adopt a new theory, it better encompass all of our older observations.

My weight was:

W = mg = 80 kg * 10 m/s^2 = 800 N

We use 10 for g, because calculators must be weened and then reintroduced. NEW THEORY:

F_G = \frac{6.67E-11*80kg*6E24kg}{(6.4E6)^2}=784 N

That’s pretty close. If we’d of used 9.81 and hadn’t rounded some other figures, we’d be even closer. At this point, the invitation to this material wears out. I can’t really pull Saturn closer to show how the inverse square really matters, although, God knows I’ve tried.

So, I switch to modeling. I want the students to get a feel for gravity, orbits, and the like. The first place we start is here. I don’t know the guy who wrote this, but it’s totally awesome.

Wait to be underwhelmed by the program I wrote.

This simulation can get out of hand quickly, so I wrote a much crappier JavaScript version. The goal here was to create something controlled, but what struck me at the last moment was that the programming is actually what matters. I had the kids steal my code (View Source), and then had them change the values for the gravitational force or whatever. It was kind of a weird playground where they would break stuff, fix stuff, and make things act strangely. I’ve never had so many kids connect to how their video games work before (and why Mario can jump 8 times his own height).

Here’s the code that matters. The kids had fun changing numbers and adding masses.

Y = parseInt(testMass.style.top);
X = parseInt(testMass.style.left);

dY = Mass1Y-Y; // negative if lower than mass
dX = Mass1X-X; // negative to the right of mass

dX2 = Mass2X-X; // negative to the right of mass
dY2 = Mass2Y-Y; // negative to the right of mass

r = Math.sqrt(dY*dY+dX*dX); //radius to larger Mass
r2 = Math.sqrt(dY2*dY2+dX2*dX2); //radius to larger Mass2

theta = Math.atan(Math.abs(dY/dX)); //angle to Mass from x axis
theta2 = Math.atan(Math.abs(dY2/dX2)); //angle to Mass2 from x axis

a1 = 2000/(r*r); //acceleration given by universal law of gravity
a2 = 2000/(r2*r2); //acceleration given by universal law of gravity

aX = a1*Math.cos(theta); //acceleration in x direction
aX2 = a2*Math.cos(theta2); //acceleration in x direction

aY = a1*Math.sin(theta); //acceleration in y direction
aY2 = a2*Math.sin(theta2); //acceleration in y direction

I think I’m going to add in equipotential lines from the red masses, and make the whole thing look prettier, but hey, I’ve got a newborn.

Where’s the Inquiry?

The questions start rolling in at this point, which is all I’ve ever wanted for Christmas. The inquiry tends to take the form of short bursts and starts. Breaking from my normal mode (small independent groups), I tended to marshal the class into doing a lot of short investigations.

This time around, a student asked if Jupiter was slower because it was so big. This turned into a class period of deriving orbital speeds from NASA data tables. (No, it’s mass doesn’t matter, just it’s distance from the Sun)

The next class period we took our discussion to flying a spaceship towards Jupiter. I was forced to lecture about escape velocity under threat of mutiny if I didn’t (This is when direct instruction works). We read from 2001: A Space Odyssey, specifically the chapter about the Transit of Jupiter. We listened to some radio noise, we laughed, we cried, we feared HAL, it was great.

This led us to special relativity and general relativity, which is where we are now. They find this material compelling enough and hard enough to grapple with, that we spend of alot of time silently staring at each other; small grunts and half phonemes get uttered, but they are usually followed by cast-down eyes and furrowed brows. Such is relativity and the breaking of time.

Things open up much more when circular motion comes into play. We’ve met the most famous of the common centripetal forces: gravity. The guided investigation involves spinning a weight on a string that runs through a tube and is anchored by a much heavier weight. This a crappy solar system — and I have given it the illustrative treatment it is due — but nevertheless demonstrates the relationship between velocity and radius when moving in circles.

The open investigations go crazy:

  • How fast can Jello spin? (Gelatin concentration vs. internal centripetal forces)
  • Artificial Gravity Swimming Pool (Angular Speed on swimming pool surface angle)
  • The Cavendish Experiment gets attempted (and succeeds about every other year)
  • Underarmor Space-time sheet

Shawn Cornally • December 1, 2010


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